Related papers: Model order reduction by convex displacement inter…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
One little-explored frontier of image generation and editing is the task of interpolating between two input images, a feature missing from all currently deployed image generation pipelines. We argue that such a feature can expand the…
Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…
This paper presents a novel multilevel projection-based stabilization method for advection-dominated convection--diffusion problems within the framework of Isogeometric Analysis. The proposed approach extracts and penalizes fine-scale…
A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…
We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling…
Video frame interpolation aims to synthesize one or multiple frames between two consecutive frames in a video. It has a wide range of applications including slow-motion video generation, frame-rate up-scaling and developing video codecs.…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms of accuracy. In fact, pointwise interpolation of such solutions is rarely efficient and leads generally to incorrect…
Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then…
In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…